Question: Rewrite as a simplified fraction. ${0.9\overline{63} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 963.6363...\\ 10x &= 9.6363...\end{align*}}$ Subtracting the two equations, we have: ${990x = 954}$ ${x = \dfrac{954}{990}} $ ${x = \dfrac{53}{55}} $